Cyclotron coils design rules

To produce a field B of 1 weber/m2 (10 kilogauss) in a gap of 10 cm length, the number of ampere-turns required is 7.95 x 10^4 ... At 18 kilogauss ... the observed value of B is 0.73 of that predicted.

Livingston & Blewett, Particle Accelerators (1962) — p. 258-260

Editorial note, tabletop extrapolation: At the reference machine's 5.9 kG the ideal formula is a good first estimate (~1.7e4 ampere-turns across its 3.6 cm gap) before iron reluctance and leakage add their share - FEMM closes that gap. Field headroom is cheap while the iron stays unsaturated and expensive after; where the knee sits is a property of the specific circuit, not a universal 10 kG line.

a common phenomenon ... is to find the median plane dished into a shallow saucer shape caused by asymmetries in the magnet iron or of the reinforcing iron in the foundations. A similar shape will result if the coils are not located symmetrically or if there is a shorted turn. ... At MIT such a 'dished' median plane was corrected by connecting an external resistor in parallel with one of the coil layers, which reduced the current in this layer and in this case had the effect of flattening the median plane.

Livingston & Blewett, Particle Accelerators (1962) — p. 288

Editorial note, tabletop extrapolation: Rebar in the floor or a nearby steel bench can dish an H-frame tabletop field; remove or symmetrize nearby steel first where practical, then trim electrically (a rated shunt across one accessible layer, as MIT did) rather than re-machining.

The magnet consists of coils of hollow copper tubing wound on a two-ton core of mild steel. ... capable of producing a very uniform 17,000 gauss field ... tapered from 12-inch pole stems to 10-inch pole faces.

McGuire, The Iowa State University 1.5 MeV Undergraduate Cyclotron (1961) — p. PDF 7 (printed 479) carries the quoted 20 kW sentence; the magnet paragraph is on PDF 5 (printed 477) and Table 1 on PDF 9 (printed 481)

Editorial note, tabletop extrapolation: Sets the scale of the jump from the reference machine's 0.59 T solid-tubing magnet toward a 1.5-1.7 T machine: at multi-kilowatt dissipation, hollow conductor with water flow is the usual regime (dg-092). The exact power for a next machine depends on its actual gap, field and copper budget - the magnet-power calculator sizes it, this precedent scales it.

we used the basic equation for an electromagnet... we decided a 2.13'' gap a reasonable size... we then concluded that we needed 720 turns to reach 1.6T.

Heuer & Baumgartner, Design of a 2 MeV Cyclotron (2009) — p. 32

Editorial note, tabletop extrapolation: The same sizing equation the reference machine's magnet obeys (its 538 turns are that build's own number, not this source's). The gap-only formula is the floor; the source's ~15% surplus is a realistic allowance for what it omits, and FEMM confirms the actual requirement (dg-016).

Bair = mu0 NI / (g + lambda/mu); ... Approximation ignoring iron reluctance (lambda/mu << g): NI = B g /mu0

Marks, Conventional Magnets for Accelerators — CAS lecture (2004) — p. 25

Editorial note, tabletop extrapolation: The correction term is one contributor that bends the excitation curve at high current: comparing measured B-vs-I against the lumped formula flags when the iron starts stealing amp-turns - attributing the bend among saturation, leakage and fringing then belongs to FEMM, which the lumped model cannot do.

Given the field = B0, pole width = a, Magnet Length = L and ramp time dt, the only design option available for changing the voltage is the number of turns, N.

Tanabe, Iron Dominated Electromagnets, Lecture 10: Forces, Stored Energy, Fringe Fields, End Chamfering (2005) — p. 12-16

Editorial note, tabletop extrapolation: Quick check on a next machine's supply matching: stored energy in a 10-inch, 1 T, 5 cm gap magnet is about 1 kJ from the gap alone (B^2/(2*mu0) x volume; fringe fields add more), and turn count trades current for voltage against whatever surplus supply the builder finds.

Note that all regions must close, that is the first and last coordinates are equal ... Negative currents in the right hand coil gives positive flux on the horizontal centerline.

Tanabe, Iron Dominated Electromagnets, Lecture 4: POISSON — A Two-Dimensional Magnetostatic Solver (2005) — p. 9

Editorial note, tabletop extrapolation: The two mistakes that make a first POISSON run fail; also shows amp-turns (not turns and amps separately) are what the model needs.

efficiency ~ 0.98 For magnets with well designed yokes.

Tanabe, Iron Dominated Electromagnets, Lecture 6: Excitation, Coil Design, System Design and Water Flow (2005) — p. 4-6, 12

Editorial note, tabletop extrapolation: Lets the builder size a next machine's amp-turns by hand before any FEA - with the ~2% read correctly: it is the yoke's MMF consumption in a well-designed magnet, not the accuracy of the estimate. Saturation, the real B-H curve, leakage and geometry can move the answer by far more than 2%, which is what the FEMM pass is for.

The electrical bussing connection creates a loop around the beam line, resulting in a small solenoidal field... the in and out conductors should be placed close to each other.

Tanabe, Iron Dominated Electromagnets, Lecture 8: Core Fabrication, Assembly, Installation and Alignment (2005) — p. 24-26

Editorial note, tabletop extrapolation: Cheap to get right on a next machine: dress the coil leads as a twisted/adjacent pair and keep supply cables from encircling the chamber.

coil cooling estimation: dT(C) = 60*P(kW)/(4.19*N(l/min))

Zaremba, Magnets for Cyclotrons (2005) — p. 30-32

Editorial note, tabletop extrapolation: The cooling formula is immediately usable: a next machine's 5 kW coil at 4 L/min runs ~18 C water rise; the flutter formulas matter only if the builder adds sector (AVF) pole faces.

where h is the magnet gap height in [m] ... eta is the efficiency (typically 99%), mu_0 is the permeability of free space ... Note that Eq. (5) is only approximate and neglects fringe fields and iron saturation.

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 15

Editorial note, tabletop extrapolation: First-cut sizing for a next machine: at a 2 cm gap and 1.0 T, ~8000 A-turns per pole sets conductor and current-density scale before any FEMM run - the floor that FEMM then corrects for fringe and saturation.

U_magnet = U_gap + 2 U_coil + U_yoke = B^2/(2 mu_0) (V_gap + 2 V_coil/6 + (1/mu_r) V_yoke)

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 18

Editorial note, tabletop extrapolation: Tells you the inductance scale and therefore how fast a bench supply can ramp the magnet and how big the flyback/dump protection must be (dg-218) - computing the protection against the worst-case inductance across the operating range, not the single linear figure.

l_avg = pole perimeter + 8 x clearance between pole and coil + 4 x coil width

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 27, 33

Editorial note, tabletop extrapolation: Gives copper length, hence resistance and power, straight off a sketch - exactly what a garage builder needs before ordering tubing.

the maximum current density for voluminous coils which are almost entirely enclosed in the magnet yoke should not exceed 1 A/mm2 ... The current density in direct water-cooled coils can be typically as high as 10 A/mm2.

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 28-29, 31

Editorial note, tabletop extrapolation: The reference machine's 538-turn solid copper tubing coils sit in the air-cooled regime; unless they qualify as small and thin enough to shed heat (the source's 2 A/mm^2 case), the quoted limit for enclosed coils is 1 A/mm^2 - going higher means hollow conductor with water flow.

The velocity of the cooling medium ... should be sufficiently high to guarantee a turbulent flow but low enough (u_avg <= 5 m/s) to avoid erosion and vibration. A maximum permitted temperature of less than 60 C on the coil surfaces was found to be good practice.

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 31

Editorial note, tabletop extrapolation: Hard numbers for a home chilled-water loop as DESIGN limits, not damage cliffs: hold velocity under ~5 m/s (erosion and vibration risk grow beyond it), coil surfaces under 60 C (insulation aging accelerates with temperature), and note the arithmetic - a 30 C inlet plus 30 C rise means up to 60 C outlet water, consistent with the surface limit but tight in a hot garage: derate for your ambient.

Q_water = 2.388 x 10^-4 P/dT ... d = 5.59 x 10^-3 (P/(dT Kw))^0.368 (l/dp)^0.21

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 32-34

Editorial note, tabletop extrapolation: Lets the builder compute the hollow-conductor bore and pump requirement for a next machine's 5-20 kW magnet with a spreadsheet, no CFD - provided every input is converted to the source's units first: a bar-for-pascal slip in the pressure drop moves the bore answer far more than the recipe's real margin.

NI_dipole = Bh/(eta*mu0), where the magnet efficiency, eta... The magnet efficiency for a well designed yoke is eta >= 98%.

Tanabe, Iron Dominated Electromagnets: Design, Fabrication, Assembly and Measurements — SLAC-R-754 (2005) — p. 116-117, 129

Editorial note, tabletop extrapolation: One-line check of the reference machine's 538 turns: at 0.59 T and its gap the formula predicts the required current within a couple percent if the H-frame iron is unsaturated. A measured efficiency well below the formula's ~98% says the model is missing something - saturation, leakage, a parasitic joint gap, or a wrong effective-gap value - and FEMM sorts out which.

production of a field of 1 T in a gap with a 0.02 m spacing requires 16-kA turns (160 turns of wire if a 100-A supply is available).

Humphries, Principles of Charged Particle Acceleration (1986) — p. 111

Editorial note, tabletop extrapolation: Numerically the builder's own worked example: 538 turns at ~30 A across the reference machine's 1.42-in (3.6 cm) gap predicts ~0.56 T from the ideal gap formula - an upper bound, because real iron reluctance and leakage only subtract from it. The measured shortfall from ideal maps those losses; FEMM attributes them.

Ampere-Turns = 2.02 x gauss x inches gap

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 13

Editorial note, tabletop extrapolation: Directly applicable: 5900 G across a 2-inch gap needs ~24,000 ampere-turns as the ideal floor, with iron reluctance and leakage added on top (dg-016, dg-036). Leakage multiplies the FLUX the iron must carry - that sizes the yoke - not the gap MMF this formula computes.

the magnetic field actually increases in magnitude out to around r = 5 cm at which point it begins decreasing again. This is problematic because it yields a negative field index

Morrow, Focusing in the Houghton College Cyclotron — Houghton College thesis (2015) — p. 51-53

Editorial note, tabletop extrapolation: A concrete trap when adding iron or coils near the center of an 8-inch pole: check the sign of dB/dr over the whole usable orbit range, not just at the edge - the 5 cm crossover and the -0.1 index are that geometry's numbers, not general thresholds.

the difference in radius is minimal - about 0.2 cm - and comes at the steep cost of a ~20% reduction in maximum magnetic field from 1.27 T to 1.07 T. As such, this modification was considered insufficient.

Morrow, Focusing in the Houghton College Cyclotron — Houghton College thesis (2015) — p. 53-54

Editorial note, tabletop extrapolation: Saves a next machine's builder from spending months on one class of trim-coil fix inside a small gap (they also steal gap height) - but this is one modelled geometry: evaluate any other trim-coil design from its full B(r) map and orbit dynamics.

A Haskris H-4057 water chiller, capable of 3.8 L/min (1.0 gpm) ... Since the diffusion pump requires at least 0.8 L/min, the maximum that can be supplied to the magnet is 3.0 L/min ... the magnet requires 6.1 L/min

Loucks, Initial Results from the Houghton College Cyclotron — Houghton College thesis (2007) — p. PDF p.36 = printed p.36 (Loucks thesis Sec. 3.2 Magnet); the cited '35-36' range is correct, all figures are on 36

Editorial note, tabletop extrapolation: Do the L/min bookkeeping for the whole next machine (magnet + diffusion/turbo + RF amp) before buying a chiller; the cooling loop is a first-class design constraint, not an afterthought.

With the chamber in place, the separation between the pole tips is 3.81 cm, giving a maximum magnetic field of 1.28 T at 70 A ... requiring 18 C water flowing at 0.8 gallons per minute (at 50A)

Yuly, The Houghton College Cyclotron: a Tool for Educating Undergraduates — Cyclotrons 2013, WE1PB01 (2013) — p. 2-3

Editorial note, tabletop extrapolation: A purchasable-magnet benchmark almost exactly at the reference machine's scale. The 0.8 gpm is a flow figure, not a chiller spec: size the chiller from coil dissipation and allowable temperature rise (P = flow x heat capacity x dT - the magnet-power calculator's territory), with the flow number as the plumbing constraint it is.

The magnet's upper and lower coils are independently energized enabling an intentional axial field imbalance so as to vertically shift the accelerating plane.

Koeth, Undergraduate Education with the Rutgers 12-Inch Cyclotron (2015) — p. 2

Editorial note, tabletop extrapolation: Cheap beam-height trim for a next machine: two supplies, or a properly rated current-trim circuit on one coil, instead of re-machining anything - verify the result with a field or beam measurement, since unequal excitation perturbs the midplane symmetry it exploits.

Cited in: Beam Dynamics: An Interactive Laboratory

Trim coils increase the gap ... Very weak except in superconducting machines ... Model it before implementing it to avoid unexpected effects

Beeckman, Cyclotron Magnets — ECPM37 lecture, Groningen (2009) — p. 33, 47

Editorial note, tabletop extrapolation: Settles the shim-vs-trim-coil question for a small warm magnet the way the Houghton thesis found empirically: iron wins for the main profile. A weak trim coil can still earn a place for fine, reversible adjustment where the gap budget allows one.

the field B = mu0 nI/h is proportional to the total current in the solenoid, is inversely proportional to the magnetic gap and is independent on the pole surface, a rather counter-intuitive fact to most people.

Beeckman, Cyclotron Magnets — ECPM37 lecture, Groningen (2009) — p. 70-71

Editorial note, tabletop extrapolation: The core sizing identity for a home magnet, in its regime (unsaturated iron, h the total effective gap): field follows ampere-turns over gap, and bigger poles alone buy nothing. Shaving the gap buys field at the price of chamber, dee and beam clearance (dg-163's trade) - cheap, not free.

By means of auxiliary coils wound on the pole pieces it is possible to control the position of the beam with respect to the median plane of the tank. The coils consist of 65 turns of #6 wire wound on each pole piece. A dc power supply provides up to 75 amperes

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 35

Editorial note, tabletop extrapolation: Cheap and direct for a next machine: an auxiliary winding on the poles gives a vertical-centering knob instead of mechanical re-shimming - size its ampere-turns from the field asymmetry the orbit calculation asks for (the 86-inch used up to ~4900 A-turns; a small machine needs proportionately less, but compute it), with a reversible supply and thermal check.

Cited in: Beam Dynamics: An Interactive Laboratory

power varies inversely with volume of conductor, so to a first approximation it can be chosen at will ... a well-designed coil will have a 'packing ratio' greater than 0.5.

Livingston & Blewett, Particle Accelerators (1962) — p. 273-277

Editorial note, tabletop extrapolation: If a next machine's coils run hot, more copper is a fix on equal footing with more cooling: doubling conductor volume halves dissipation at the same ampere-turns - paid for in coil size, weight and winding-window space.

The voltage breakdown strength of a resin-impregnated layer of glass cloth or cotton mesh is usually over 100 volts/mil ... necessary to utilize mica-sheet or mica-flake insulation to obtain the higher voltage-to-ground insulation.

Livingston & Blewett, Particle Accelerators (1962) — p. 278

Editorial note, tabletop extrapolation: Potting the reference machine's coils stops the slow insulation abrasion that coil hum causes. The >100 V/mil figure is the source's historical material datum, not an allowable design stress: size insulation from maximum turn-to-turn and coil-to-ground voltage with margin for voids, transients, creepage and temperature - the quote itself reserves voltage-to-ground duty for mica - and prove the finished coil with a hipot test rather than resting on the coupon number.

The conductivity is maintained at 10 micromhos or less, with a pH of about seven. Dee system water temperature stability of 1 F or better is required for steady operation.

Ramler & Parker, The Argonne 60-Inch Cyclotron — ANL-5907 (1959) — p. 6

Editorial note, tabletop extrapolation: Two portable METHODS, not specs: monitor conductivity and pH on any hollow-conductor DI loop, and stabilize dee-water temperature if a next machine water-cools the dee (the RF tune walks with dee temperature). Set the actual limits from conductor material, voltage to ground, and measured RF drift, not from ANL's numbers.

The circulating pumps and heat exchanger are sized to handle a 1000-kw heat load, with the normal operating load being about 300 kw.

Ramler & Parker, The Argonne 60-Inch Cyclotron — ANL-5907 (1959) — p. 6

Editorial note, tabletop extrapolation: For a next machine dissipating 1-5 kW, real margin over normal load is what makes long runs boring - ANL carried about 3x; pick your own factor from duty cycle, ambient conditions and fouling allowance rather than copying the ratio.

It is necessary for the secondary coil to be cooled with oil or deionized water... because even minute thermal expansion of the copper can change the inductor's value.

Heuer & Baumgartner, Design of a 2 MeV Cyclotron (2009) — p. 23

Editorial note, tabletop extrapolation: Explains RF drift during long runs at the reference machine's power levels; cooling the tank coil stabilizes tune.

When properly cooled, our 1/4''x1/4'' hollow copper conductor can safely carry up to 120A. Allowing a margin of safety, we designed our magnet to operate at 110A.

Heuer & Baumgartner, Design of a 2 MeV Cyclotron (2009) — p. 32

Editorial note, tabletop extrapolation: A conductor rating like this is conditional on the cooling that produced it - wall thickness, bore, flow, inlet temperature - so treat it as one documented data point for hollow-conductor coils, not a transferable ampacity. Rate a next machine's conductor from its own cooling calculation; the coil-geometry and magnet-power calculators cover the resistive side.

Using this type of winding allows for a more uniform field than a simple spiral winding.

Heuer & Baumgartner, Design of a 2 MeV Cyclotron (2009) — p. 32-33

Editorial note, tabletop extrapolation: A rebuild of the reference machine's 538 turns as potted double-pancakes with a cooling manifold is an attractive concept - as a design study: pancake count, potting, parallel water paths and repairability are engineering choices needing their own magnetic, hydraulic and thermal analyses, not properties the source's uniformity comparison confers.

Our magnet can achieve a maximum temperature of 173 oF and will normally operate at no more than 142 oF.

Heuer & Baumgartner, Design of a 2 MeV Cyclotron (2009) — p. 33

Editorial note, tabletop extrapolation: Set a next machine's potted-coil design point from the resin system's rated thermal class and a modeled or measured hotspot with margin for cooling failure - not from another magnet's numbers. Note 61 C at ordinary ambient is already a 36-41 C rise, looser than Tanabe's ~30 C-rise guidance for long potted-coil life.

The value of number of turns (N) is chosen to match power supply and interconnection impedances.

Marks, Conventional Magnets for Accelerators — CAS lecture (2004) — p. 35-36

Editorial note, tabletop extrapolation: The reference machine's 538 turns were set by its supply; for a next machine, pick the surplus supply first and wind N = NI_required/I_supply - then check voltage compliance, inductance (and its dump-path consequences, dg-218) and cooling before committing.

Power distribution cables... are generally limited to a current density of <1.5 to 2 Amps/mm2.

Tanabe, Iron Dominated Electromagnets, Lecture 6: Excitation, Coil Design, System Design and Water Flow (2005) — p. 21

Editorial note, tabletop extrapolation: An orientation point, not a coil rating: magnet coils differ from distribution cables in bundling, enclosure and heat path. The coil-specific limits are dg-092's - voluminous enclosed coils are held to 1 A/mm^2, and water cooling is what opens the range upward.

the optimum is flat and appears to be j=4 Amps/mm2. However, a higher design value (the canonical j=10 Amps/mm2 value) is generally chosen.

Tanabe, Iron Dominated Electromagnets, Lecture 6: Excitation, Coil Design, System Design and Water Flow (2005) — p. 29-30

Editorial note, tabletop extrapolation: For a home machine the source's trade often runs toward the low end: hand-wound coils and metered power favor the ~4 A/mm^2 economic optimum, and the reference machine's tubing coil runs lower still. Window space and magnet size push the other way - which is why the canonical 10 exists - so do the two-line cost comparison for your own copper and power prices.

f = 64/Re for laminar flow Re < 2000. For turbulent flow (Re>4000), the friction factor is gotten by solving a transcendental equation.

Tanabe, Iron Dominated Electromagnets, Lecture 6: Excitation, Coil Design, System Design and Water Flow (2005) — p. 32-34

Editorial note, tabletop extrapolation: The straight-passage core of hydraulic sizing for any hollow-conductor or tubing-wound coil - add bends, fittings and manifold (minor) losses on top, and confirm with a flow test; the formula alone is the floor, not the whole recipe.

Desirable temperature rise... < 10 deg. C. Maximum allowable temperature rise (assuming 20 deg. C. input water) < 30 deg. C for long potted coil life.

Tanabe, Iron Dominated Electromagnets, Lecture 6: Excitation, Coil Design, System Design and Water Flow (2005) — p. 40, 45

Editorial note, tabletop extrapolation: One-line flow-rate calculator: a 1 kW coil on a next machine needs ~0.4 gpm for a 10 C rise.

For water velocities > 15 fps, flow vibration will be present resulting in long term erosion of water cooling passage.

Tanabe, Iron Dominated Electromagnets, Lecture 6: Excitation, Coil Design, System Design and Water Flow (2005) — p. 42

Editorial note, tabletop extrapolation: The cited source's upper design guideline when sizing pump and passage diameter for a hollow-conductor coil; onset of vibration and erosion also depends on bend severity, passage geometry, material and water chemistry, so use a lower limit where conductor-manufacturer guidance or testing warrants.

Pressure drop can be decreased by a factor of eight if the number of water circuits are doubled.

Tanabe, Iron Dominated Electromagnets, Lecture 6: Excitation, Coil Design, System Design and Water Flow (2005) — p. 47

Editorial note, tabletop extrapolation: Argues for manifolded pancake sub-coils on a next machine instead of one long series water path through 538 turns.

If the design hole diameter is increased, the required pressure drop is decreased dramatically. If the fabricated hole diameter is too small... pressure drop can increase substantially.

Tanabe, Iron Dominated Electromagnets, Lecture 6: Excitation, Coil Design, System Design and Water Flow (2005) — p. 48

Editorial note, tabletop extrapolation: When choosing hollow conductor for a next machine, weigh bore against copper cross-section (a bigger hole raises electrical resistance) and flow-test each pancake before potting - the fabricated bore, not the drawing, sets the pressure drop.

A single water circuit in a coil assembly should be wound from a single continuous length of conductor. Splices 'buried' within the potted insulation should not be allowed.

Tanabe, Iron Dominated Electromagnets, Lecture 9: Coil Fabrication, Testing and Electrical Safety (2005) — p. 14-16

Editorial note, tabletop extrapolation: For a next machine wound from copper refrigeration tubing: buy one continuous coil per water circuit, keep the shop swarf away from the winding, and verify the bore is clear before the tubing is buried in the stack.

This test can only be performed on a coil isolated from metallic surfaces and will not work once the coil is installed on the core. ... the iron permeability will mask the expected behavior of the electrical circuit.

Tanabe, Iron Dominated Electromagnets, Lecture 9: Coil Fabrication, Testing and Electrical Safety (2005) — p. PDF p.18 (slide deck, unnumbered); procedure on PDF p.17, hipot/QA context pp.19-20

Editorial note, tabletop extrapolation: A pulse source, capacitor and scope let the builder screen the next machine's coils before they are trapped under the yoke - run the impulse test during fabrication, before the coil goes on the core, and photograph the low- and high-voltage waveforms as the baseline. Both tests put hazardous voltage on the coil: use rated, current-limited test gear, discharge and ground between steps, and keep others clear.

Water flow calculations made for the preliminary design may be unreliable for a coil designed with many tight turns... due to the added flow impedance of tight radius turns.

Tanabe, Iron Dominated Electromagnets, Lecture 9: Coil Fabrication, Testing and Electrical Safety (2005) — p. 25

Editorial note, tabletop extrapolation: A bucket-and-stopwatch flow test at operating pressure is the real spec for the reference machine's 538-turn tubing coil (many turns; check its bend radii against the passage size). Record water temperature - viscosity matters most if any branch runs laminar - and measure each parallel branch separately, since a total-flow test hides an imbalance.

Water hoses should be at least one meter long and use nonconducting material to prevent current leakage from the magnet. The water “in” fittings should be smaller than the water “out” fittings ... If a flow interlock (orifice plate) is used, it should be attached to the return manifold.

Tanabe, Iron Dominated Electromagnets, Lecture 9: Coil Fabrication, Testing and Electrical Safety (2005) — p. 3

Editorial note, tabletop extrapolation: The reference machine's water-cooled copper-tubing coil sits at supply potential; a meter of non-conducting hose per lead limits leakage current, and an interlock on the return detects a blocked circuit - cheap practices worth copying at home scale. They reduce specific risks; they are not shock protection as a whole, which still rests on earthing and supply-side protective devices.

The normal set-point of Klixons is about 89 C. It will generally reset at about 70 C ... One thermal interlock is installed on each water circuit ... All the interlocks on one magnet are connected in series. ... The Klixon is preferably mounted on the water return lead of the coil ... always mounted on the current carrying portion of the conductor ... mounted to a block hard-soldered to the conductor.

Tanabe, Iron Dominated Electromagnets, Lecture 9: Coil Fabrication, Testing and Electrical Safety (2005) — p. 5-7

Editorial note, tabletop extrapolation: A thermal snap-switch soldered to the coil exit tube, wired in series with the supply enable, is cheap, high-value protection against cooking a winding on a lost-water event - alongside the flow interlock (dg-202), not instead of it. Set-point and switch rating are the designer's to verify against the winding's own insulation limit.

ordered blank or pre-impregnated with varnish (0.02 ≤ t ≤ 0.1 mm) or half-overlapped polyimide (Kapton®) tape (0.1 ≤ t ≤ 0.2 mm) ... a filling factor between 0.63 (round) to 0.8 (rectangular) can be obtained.

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. PDF 29 (printed 93) for the quoted sentence; PDF 28-29 (printed 92-93) for the varnish/Kapton/filling-factor figures

Editorial note, tabletop extrapolation: Sets expectations for how much winding window the insulation eats on a hand-wound 538-turn coil - then compute the actual packing factor from the chosen conductor's finished insulated dimensions and the real winding layout, since fill depends on shape, pattern and voids, not on insulation thickness alone.

For a bending radius of three times the conductor width we can expect a keystoning of 3.6% ... we can ignore the effect of keystoning by systematically choosing a bending radius four times larger than the conductor width.

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 30

Editorial note, tabletop extrapolation: For bending round copper tubing on a homemade coil the analogous risks are ovalization and bore pinch: use tube-specific minimum-bend-radius and ovality limits (diameter, wall, temper and tooling all matter), inspect or flow-test the formed passage, and watch the insulation at the bends.

An aspect ratio of c:b between 1:1 and 1:2 should be chosen, and the packing factor fc somewhere between 0.6 and 0.8.

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 33

Editorial note, tabletop extrapolation: Turns the amp-turn number into an actual coil window size before you buy tubing or start winding.

This implies that for a given flow, the pressure drop is reduced by a factor of eight by doubling the number of cooling circuits.

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 33

Editorial note, tabletop extrapolation: Explains why splitting a big coil into 2 or 4 hydraulic circuits lets a garage chiller pump do the job - under the model's conditions: total flow and total conductor length fixed, circuits dividing both equally; then pressure drop falls as the cube of the circuit count. Confirm the friction regime still holds after the split.

Water resistivity higher than 0.1x10^6 Ohm m; pH-value between 6 and 6.5; dissolved oxygen below 0.1 ppm

Zickler, Basic Design and Engineering of Normal-Conducting, Iron-Dominated Electromagnets — arXiv:1103.1119 (2010) — p. 34

Editorial note, tabletop extrapolation: If a next machine uses water-cooled coils at supply potential, ordinary tap water misses all three quoted limits. A deionizing cartridge loop is the standard way to hold resistivity, but the spec is three-dimensional - oxygen and pH need their own control - and the source pairs the water spec with filters near the magnet.

power distribution cables are convectively cooled and are limited to <= 1.5 Amps/mm2

Tanabe, Iron Dominated Electromagnets: Design, Fabrication, Assembly and Measurements — SLAC-R-754 (2005) — p. 128-129

Editorial note, tabletop extrapolation: For the reference machine's circuit: any leg - bus, jumper, lead - running above ~1.5 A/mm^2 without an engineered cooling path will run warm, so size leads generously. Above the line the options are any real cooling: water, forced air, conductive sinking, or intermittent duty with temperature monitoring (dg-220).

Normally, a good value for the current density is j = 10 Amps/mm2 for water cooled coils... The value of the packing fraction is typically f ~ 0.5 for small conductors.

Tanabe, Iron Dominated Electromagnets: Design, Fabrication, Assembly and Measurements — SLAC-R-754 (2005) — p. 129

Editorial note, tabletop extrapolation: Lets the builder size a next machine's coil cross-section on one sheet of paper: gross winding area ~ NI/(j*f) = NI/5 mm^2 for water-cooled copper - a first pass the thermal calculation then confirms, and the 10 A/mm^2 presumes genuine water cooling (dg-092's geometry conditions).

Flow velocity should be high enough so that the flow is fully turbulent, Re ≳ 4000... For synchrotron radiation accelerators where beam stability depends on temperature stability, ∆T ≲ 15°C.

Tanabe, Iron Dominated Electromagnets: Design, Fabrication, Assembly and Measurements — SLAC-R-754 (2005) — p. PDF pp. 134-135 = printed pp. 134-135 (chapter section 'Coil Cooling'), as cited

Editorial note, tabletop extrapolation: Direct water-cooling design window for a next machine's hollow-conductor coil; also warns that a lazy laminar-flow circuit cools far worse than the handbook film coefficient suggests.

Kilowatt-Tons = (0.118)Cu (Mega-ampere turns)^2 (inches mean turn length)

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 13

Editorial note, tabletop extrapolation: Directly applicable trade study tool: the product of coil dissipation and coil weight is fixed by NI and geometry, so more copper always buys less heat.

The coils should be wound so that they occupy approximately a rectangular cross section around the poles ... Either too flat or too tall a coil intercepts more leakage flux and thus wastes turns.

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 3

Editorial note, tabletop extrapolation: Directly applicable guidance for a next machine's coil geometry.

operate close-wound naturally air-cooled coils at a current density not exceeding 750 amps per square inch of conductor area. For intermittent operation this may be raised to 1000 amps per sq. in.

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 3

Editorial note, tabletop extrapolation: Directly applicable thermal sizing for coils matching the quoted conditions - close-wound, naturally air-cooled: 750 A/in^2 continuous, 1000 intermittent. A different winding style (open spacing, forced air, tubing with internal flow) carries different limits - dg-092's geometry table is the map.

Most coil designs favor large conductor areas and correspondingly high amperages; this reduces total voltage and simplifies both the insulation and the winding problems.

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 3

Editorial note, tabletop extrapolation: Directly applicable when choosing wire gauge and supply for a next machine's coils.

flat donuts of 1/16 in. copper sheet ... During operation cold water is run through this set of pipes; together with a large fan for general circulation, such coils should operate steadily at 1300 amps per sq. in.

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. PDF p.4 (printed -5-); comparative current-density framing on PDF p.3 (printed -4-)

Editorial note, tabletop extrapolation: A cheap construction to reach for when a next machine's pancake coils run hot: 1/16-inch copper donut plates with soldered edge tubing between pancakes. The 1300 A/in^2 is the historical design target for that geometry, not a number to adopt - recompute I^2R, water flow and temperature rise, the thermal path through the insulation, and solder and tube reliability, then measure winding temperature in operation. [Note revised 2026-08-23: earlier note called it a directly applicable upgrade that 'nearly doubles' allowable excitation.]

These windings saturate the iron (~20 KG) at somewhat less than ten amperes; at this current the temperature becomes excessive in less than an hour

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 4

Editorial note, tabletop extrapolation: Directly applicable cautionary datum: quote coil ratings as (current, time-to-overheat) pairs, not just maximum field.

The magnet coil circuit must never be broken at high currents, of course, unless adequate surge protection is provided.

Wouters, General Recommendations for Design of Small Cyclotrons — UCRL-476 (1949) — p. 5

Editorial note, tabletop extrapolation: Directly applicable: any magnet coil whose stored energy exceeds a few joules needs a dump path across the winding - freewheel diode, varistor, or resistor - rated for the coil's stored energy, peak current and clamp voltage. Without one, opening the circuit at current can arc the switchgear.

the Dee may be oscillated with voltage amplitudes of up to approximately 3000V relative to the grounded Dummy Dee. The Dee capacitance is approximately 76 pF. The secondary coil inductance of 0.87 uH or more in parallel with the Dee capacitance yields a resonance as high at 19.5 MHz, which is the maximum cyclotron frequency corresponding to 411 keV protons in the maximum magnetic field of 1.28 T. ... These inductors are 1/4 inch copper tubing, wound coaxially, with the 6 cm diameter primary coil outside the 4 cm diameter secondary coil. The inductance of the primary coil can be changed by replacing the coil with one having a different number of turns, several of which have been constructed

Yuly, The Houghton College Cyclotron: a Tool for Educating Undergraduates — Cyclotrons 2013, WE1PB01 (2013) — p. 3

Editorial note, tabletop extrapolation: Concrete worked values at the same scale, but measure your own machine's total capacitance (dee + stray + coil) and size the coil from L = 1/((2*pi*f)^2 * C_total); the swappable-primary approach lets you retune coupling without rebuilding the tank. The 411 keV is that machine's figure at its own field and extraction radius.

An alarm warns the operator when the coil temperature has reached a predetermined value, usually 70 to 80 C ... one to three hours are required for the temperature to reach equilibrium ... the maximum life of the magnet coil insulation, which the manufacturer estimates will vary with temperature as follows: [table: 79 C, 8-40 years; 87 C, 4-20 years; ... 130 C maximum allowable]

Livingston & Boch, The Oak Ridge 86-Inch Cyclotron — ORNL-1196, OSTI 4357145 (1952) — p. 33

Editorial note, tabletop extrapolation: Directly applicable: put a thermocouple in the next machine's winding and log it; a coil that is fine at 30 minutes can still cook at 2 hours. The 130 C figure is this manufacturer's rating for this insulation - a next machine's ceiling is its own insulation's thermal class.

It is important for the coils should be in the air stream of one of the cooling fans (they will run hot if not).

Buckler, Solid-State, 2-Decade, 1.25 kW Linear Amplifier — Development Notebook (2015) — p. 28

Editorial note, tabletop extrapolation: Applies to the homemade dee-tank coil: assess its RF loss and temperature under the intended loaded-Q and coupling conditions (resonator circulating current depends on Q and coupling, not on the DC feed), and give it forced air if it runs hot.

This operated normally at 65 C but when an identical coil, which had been nickel plated, was substituted, the operating temperature rose to 350 C.

Fowler, Radio Frequency Performance of Electroplated Finishes — Proc. IREE Australia (1970) — p. 4

Editorial note, tabletop extrapolation: Reject nickel-plated hardware anywhere RF current flows in the resonator, coil, or ground-return path unless the overplate is verified thick and continuous - or validate by measuring loss and temperature.

Most commercially available copper tube contains 0.015% to 0.08% phosphorus as a de-oxidising agent, so that its conductivity may range from 60% to 90% I.A.C.S.

Fowler, Radio Frequency Performance of Electroplated Finishes — Proc. IREE Australia (1970) — p. 6

Editorial note, tabletop extrapolation: Buy the tank-coil tubing as electrolytic/electrical-grade (C10100/C11000) copper with certified conductivity, not generic plumbing tube - worth roughly 6-23% lower RF surface resistance depending on where the plumbing tube fell in its range.

typically have true Q values of up to about 800. Very few practical circuits require a Q above 900. Attempting to design a coil with a True Q much over 1,000 usually results in a coil with abnormal physical dimensions

Murphy, The Elusive Q of Single-Layer Air-Core Coils — CQ Magazine, May 1999 (1999) — p. 1

Editorial note, tabletop extrapolation: Do not budget the resonant step-up on textbook thousands: measure or model the loaded Q of the actual resonator under representative coupling (loaded Q sits well below the coil's unloaded Q), then size the amplifier for 5-13 kV dees from that measurement.

the presence of the coil's distributed capacity causes the Q observed by the Q meter to be lower than the true Q of the coil

Murphy, The Elusive Q of Single-Layer Air-Core Coils — CQ Magazine, May 1999 (1999) — p. 1

Editorial note, tabletop extrapolation: For the cited Q-meter method, treat the reading as a lower bound and keep leads and fixture capacitance minimal. A VNA measurement is a different animal: state whether loaded or unloaded Q is being extracted, calibrate and de-embed the fixture, and include the distributed capacitance in the fit - VNA errors can bias either direction.

Q increases with coil diameter (see figs. 1-4). Q increases with coil length, rapidly when the L/d ratio is small ... Q increases with frequency

Murphy, The Elusive Q of Single-Layer Air-Core Coils — CQ Magazine, May 1999 (1999) — p. 1-2

Editorial note, tabletop extrapolation: At 9 MHz a 3-4 inch diameter tank coil in the charted geometries reads Q over 1000. At fixed frequency and capacitance the dee voltage scales as sqrt(P*Q) - doubling Q at the same drive buys about 40% more voltage, not double - so treat Q gains as helpful, and verify with the loaded Q actually measured.

The conductor diameter must be within the range of 0.45 and 0.70 times the center-to-center distance between adjacent turns (not all commercial stock coils meet this condition).

Murphy, The Elusive Q of Single-Layer Air-Core Coils — CQ Magazine, May 1999 (1999) — p. 2

Editorial note, tabletop extrapolation: For a 9 MHz matching/tank inductor, space the turns so the wire fills 45-70% of the pitch - close-winding bare tubing costs Q (proximity effect is the standard explanation, beyond this source's scope) - and check any stock coil against the ratio before trusting its rated Q.

Maximum Q occurs at a coil L/d ratio of between (depending on other coil design parameters) 0.35 and 0.45, decreasing rapidly below that ratio and more slowly above

Murphy, The Elusive Q of Single-Layer Air-Core Coils — CQ Magazine, May 1999 (1999) — p. 2-3

Editorial note, tabletop extrapolation: Make the resonator coil short and fat (length a bit under half its diameter), not the long skinny solenoid that fits most easily in a corner - and not a pancake either: below the optimum Q collapses quickly.

The equations do not hold for coils with a length-to-diameter ratio of less than 0.35:1, coils with less than about 4 turns, or coils with conductor diameter-to-turn spacing ratios of less than 0.45:1 or greater than 0.70:1.

Murphy, The Elusive Q of Single-Layer Air-Core Coils — CQ Magazine, May 1999 (1999) — p. 3

Editorial note, tabletop extrapolation: A 2-3 turn link or coupling loop at 9 MHz is outside the formulas; measure it rather than calculate it.

The practically achievable engineering current density (the ratio of the value of the ampere-turns in the winding to the cross section of the conductor) is of the order of 5 A/mm2.

Smirnov, The Cyclotron and Its Modeling — Phys. Part. Nuclei 52 (2021) — p. 15-16

Editorial note, tabletop extrapolation: First-cut sizing for a next machine's coil pack: NI / 5 A/mm^2 estimates the winding cross-section with water cooling - a starting point that still owes fill factor, cooling channels and insulation their space, and the thermal calculation is the real gate (magnet-power calculator). Air-cooled magnet wire derates well below this (dg-092).

The coil height giving the minimum cost was found for a field of 20,000 gauss. Since the cost curve had a flat minimum this resulted in little increase in cost.

Creutz, Design and Construction of Synchro-Cyclotron — NYO-780 (1950) — p. 8

Editorial note, tabletop extrapolation: General magnet economics in FORM: minimize steel + copper + power cost for your own prices and expect a flattish minimum near the optimum - CIT's flatness belonged to a 20-kilogauss design at 1950s prices, so re-run the small optimization with today's numbers before leaning on the flatness for convenience deviations.

Glass tape is inserted along all metal seams to prevent weld-flash from entering the can.

Creutz, Design and Construction of Synchro-Cyclotron — NYO-780 (1950) — p. 14

Editorial note, tabletop extrapolation: Directly applicable craft rule for welding on or near a next machine's coil case: glass tape or an equivalent temporary barrier keeps weld flash and spatter out of the can. It does nothing against brazing flux, molten filler or conducted heat - hot work near a wound coil also needs thermal protection and temperature monitoring, or should be finished before winding. [Note revised 2026-08-23: earlier note extended the barrier to 'any welding or brazing'.]

requires the addition of an inhibitor to reduce attack on the aluminum and steel provoked by the presence of minute quantities of copper in the water.

Creutz, Design and Construction of Synchro-Cyclotron — NYO-780 (1950) — p. 53

Editorial note, tabletop extrapolation: Directly applicable chemistry for any next machine's water loop touching Cu plus Al: pick a modern inhibitor for the actual alloy set, water chemistry and temperature - the transferable fact is that trace copper is the aggressor, so the loop needs treatment even when each metal alone would be fine.

All the adapters on the coil terminals are water cooled and supplied with thermal switches to protect the coil terminals from overheating.

Creutz, Design and Construction of Synchro-Cyclotron — NYO-780 (1950) — p. 56

Editorial note, tabletop extrapolation: Directly applicable - thermal cutouts on a next machine's coil terminals/lugs (and dee stem cooling) are cheap insurance against a loose-joint meltdown.

Weight, Fe 6 ; Cu 4 tons. Winding 3/4 in x 1/16 in strip.

Howard, Cyclotrons and High-Energy Accelerators, 1958 — ORNL-2644 (1958) — p. 106

Editorial note, tabletop extrapolation: Extrapolating down the census, an 8-in-pole machine sits in the fraction-of-a-ton class - hobby-crane scale, and the reference machine's 757 lb H-frame agrees - while every inch of added pole diameter on a next machine is bought with steeply growing steel.

Air-cooled coils. Iron ore blocks for shielding

Howard, Cyclotrons and High-Energy Accelerators, 1958 — ORNL-2644 (1958) — p. 127

Editorial note, tabletop extrapolation: Precedent that air cooling can work at this scale - two real machines did - not proof that a given coil can: adequacy is set by I^2R dissipation, winding geometry, insulation rating, duty cycle and airflow. Do the dissipation arithmetic (magnet-power calculator) and monitor winding temperature (dg-220) instead of citing precedent.

1. The resistance of the coil is proportional to its mean circumference. 2. An amount of steel approximately proportional to two times the height of one coil, plus the radial width of the coils, is required to complete the magnetic circuit.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. PDF p.25 = printed p.25 (TID-454, Sec. 1.2 Magnet Coils, 'Introduction')

Editorial note, tabletop extrapolation: The compounding is the point - on any H-frame rebuild, fat coils cost twice (copper AND the longer steel circuit around them), so invest in space factor and cooling before adding turns.

In a high-current low-voltage coil, insulation is required only to maintain mechanical separation of the conductors.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 25

Editorial note, tabletop extrapolation: What transfers is the architecture - few turns of heavy conductor at high current, direct cooling through generous passages - which beats many-turn fine-wire coils on space factor and pumping pressure. The bare-minimum insulation standard does not transfer: a modern coil wants verified turn-to-turn and ground insulation against inductive transients (dg-218's dump events), abrasion, thermal aging and coolant exposure, cheap as modern materials make it.

A second type of coil which is more attractive, when the coil must be wound at the cyclotron site, is a flat-wound helix.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 26

Editorial note, tabletop extrapolation: Directly a garage-scale construction technique: cut flat copper sectors, stack into a helix, join into a continuous conductor - no winding mandrel needed. The joints are the engineering: braze for permanent low-resistance splices, bolt only with designed contact pressure and area (the report's joint-sizing criterion: scan re-read queued for the number), and place cooling per the report's tube arrangement.

The costs which are affected are the combined costs of steel, copper, and energy.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 30-32

Editorial note, tabletop extrapolation: This collection's only explicit dollar-optimization of magnet proportions: redo the sweep with 2026 unit costs (scrap steel, surplus copper, $/kWh over expected machine life and duty cycle) - after re-reading the source for the variable definitions, since a cost formula reused without its unit system is a trap. NYO-780 p.8 did the equivalent sweep by model.

For operating convenience, the coils should be made smaller than is indicated because the total cost is a slowly varying function of the coil outside diameter near the minimum of cost.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 30

Editorial note, tabletop extrapolation: Licence to trade cost-optimality for access, cooling clearance, or stock material sizes - the optimum is a plateau, not a peak. How much plateau: evaluate the cost function at the smaller diameter and report the actual penalty rather than assuming it is a few percent. Same flat-minimum finding as NYO-780 p.8 (coil height); cite both.

It appears that the unit costs can only be determined after the cyclotron has been in operation for several years, so estimates must be employed.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 30

Editorial note, tabletop extrapolation: A 1952 statement of the plan's own doctrine, applied with modern tools: use estimated lifecycle costs with a sensitivity check on the uncertain inputs, update from quotations and commissioning actuals as they arrive, and avoid polishing the spreadsheet past its input accuracy.

It is quite clear from either equation that this factor, optimum x, depends on scale factor. The assumptions made cause the value of x given by the equation to be too large.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 31

Editorial note, tabletop extrapolation: Two cautions in one: treat big-machine coil proportions (including TID-454's own x~1.4) as non-transferable to an 8-12 in machine, and rather than mechanically shaving the computed value, redo the optimization at the actual scale with a geometry-dependent field/cost model.

One square centimeter of metallic contact distributed over the joint will carry 10,000 amps with negligible resistance and temperature rise.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 32

Editorial note, tabletop extrapolation: Bolted bus laps at amateur coil currents have huge nominal margin by this figure - but nominal lap area is not metallic contact area: oxide, pressure, fastener relaxation and thermal cycling decide the real contact. Prepare surfaces, clamp hard, lock against loosening, then verify with a four-wire millivolt-drop measurement and a full-current temperature check. A joint that passes those two tests is electrically invisible; one that hasn't been tested is a fire waiting for a loose bolt.

The generator should match the coil in the sense that the quotient of the maximum voltage output and the maximum current should be equal to the resistance of the coil.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 33

Editorial note, tabletop extrapolation: When sizing a surplus supply for the next machine's coil - or the turn count for a given supply - pick turns so the coil's HOT resistance sits at the supply's V_max/I_max corner: copper rises 20-40% in resistance from cold, so a cold-matched coil starves at temperature. And confirm the supply can actually hold its corner continuously; not every surplus unit can.

the field obtained is proportional to the inside radius of the coil and a high field can be obtained by increasing the scale ... the power p and the volume of conductor v increase with the cube of the inside radius.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 116

Editorial note, tabletop extrapolation: SCALE-SCOPED (megagauss-era context), and useful for estimating specific coils: it explains why small-bore air-core inserts and compact analyzing magnets are economically comfortable while large air-core fields carry punishing power bills - run the numbers for the actual coil rather than treating the scaling as a feasibility verdict.

For fields of 10^5 gauss and above, the situation is quite different; the power and maximum current density become important factors and more complicated designs are useful.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 122

Editorial note, tabletop extrapolation: Locates amateur work far below the exotic regime: for sub-kG correction coils, steering windings and test solenoids a simple winding is usually adequate - but 'usually' is earned by computing NI, resistance, I^2R heating, temperature rise and current density for every coil, since a small high-duty coil can be power-limited at any field. [Note revised 2026-08-23: earlier note said 'sophistication buys nothing'.]

Helmholtz coils have cross sections small in comparison with their radii squared, and thus require excessive power where a high field is required.

Foss et al., Cyclotron Component Design Technical Reports — TID-454 (1952) — p. 108

Editorial note, tabletop extrapolation: The right doctrine for any air-core uniform-field fixture - probe-calibration coils, a beamline corrector, a small synchrotron's reference field: choose the winding section from the ampere-turns, resistance, I^2R and temperature-rise arithmetic, and reach for thick optimized sections when that arithmetic shows a power problem - a classic thin Helmholtz pair is fine where it doesn't.

One of these coils consists of an insulated conductor wrapped half-way around the magnet pole piece and attached so that the pole piece completes the circuit.

Howard (ed.), Electromagnetic Research Division Semiannual, period ending 20 March 1953 — ORNL-1531 (1953) — p. 18

Editorial note, tabletop extrapolation: A field-trim knob that steers orbits without touching iron - as a modeling hypothesis for a next machine: specify ampere-turns and the return-current path, run the magnetostatic and orbit analyses (FEMM models it directly), check contact heating and forces, and only then test; variable-energy operation is a beam measurement away, not a feature to advertise from the wiring diagram.

This low field avoids saturation difficulties in the magnet iron and high excitation power requirements. Furthermore, it enables us to dispense with water cooling in the windings.

Bromley & Bruner, The Design of a Focusing and Analyzing System for the 27-inch Cyclotron Beam — NYO-3823 (1954) — p. 30

Editorial note, tabletop extrapolation: DIRECT: at a next machine's rigidity, transport-quad pole-tip fields of a few hundred gauss are plausible - compute the actual requirement from aperture, length and focal geometry (the formula) - and where field and current density land as low as the source's, unsaturated iron with air-cooled random-wound coils is exactly the regime they describe. Confirm with the dissipation arithmetic before skipping water (dg-708). OCR trap - the text layer renders the B^1/2 exponent as B^2; page image verified B^1/2.

A field of 1 kilogauss requires NI = 5000 ampere turns. As a safety factor, we have designed for 6000 ampere turns. ... Each coil will have exactly 3000 turns and the coils in each unit are connected in series

Bromley & Bruner, The Design of a Focusing and Analyzing System for the 27-inch Cyclotron Beam — NYO-3823 (1954) — p. PDF p.31 (printed page 28)

Editorial note, tabletop extrapolation: DIRECT wiring doctrine for any home-built multipole: gradient symmetry comes from forced equal current, not matched resistances - which is also why surplus-wire coil construction works, since the series circuit forgives resistance mismatch between coils.

the quantity (NI)g represents 85 to 95 per cent of the total mmf required (i.e., the efficiency ranges from 85 to 95 per cent), and Eq. 7 can be used to give a useful first approximation

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 21

Editorial note, tabletop extrapolation: The same arithmetic every H-frame designer runs today (Wouters and Zickler's CAS notes corroborate the sizing). The 85-95% efficiency band is the source's result for WELL-PROPORTIONED iron-return magnets: use it as a sanity check on FEMM excitation for a magnet in that class, and expect worse from lean yokes, corners, or parasitic joint gaps (dg-128).

the product of the power and weight of a coil conductor depends on the ampere turns and the mean diameter of the coil.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 22

Editorial note, tabletop extrapolation: The cleanest statement in this collection of the copper-vs-power trade: double the copper, halve the dissipation, at fixed NI. Lets a coil be resized on one line when a surplus supply or a heat limit is the binding constraint.

For continuous operation, 1600 amp/sq in. is about the upper limit used for oil-cooled coils. This compares with 1000 amp/ sq in. for open bus bars cooled by free convection

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 22

Editorial note, tabletop extrapolation: Brackets modern air-cooled small-magnet guidance from the 1940s operating side - mapped to the right geometry: the 2.5 A/mm^2 was for OIL-cooled calutron coils, and the 1.55 A/mm^2 for open bus bar with free-convection area a wound coil does not have. A passively cooled wound tabletop coil therefore belongs below both, in the ~1 A/mm^2 territory of the coil rules (dg-092), unless its own thermal test justifies more.

Two experimental models had values of 0.37 and 0.30, but in both cases it was necessary to use conductor sizes which were available but not specifically designed for the job.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 22

Editorial note, tabletop extrapolation: Amateur coils are usually wound from whatever magnet wire is available: budget a pessimistic 0.3-0.4 space factor when sizing the coil window, and read handbook ~0.5 figures as purpose-designed-conductor numbers.

Force on conductor (lb) = 1/1750 X kilogauss X amp X length (in.) Force between pole faces (lb) = 1/1.735 X (kilogauss)^2 X area (sq in.) Heating at center of conductor, degC = 0.00940 (Cu) / 0.00821 (Ag) X 10^6 X (inches of width of conductor)^2 X (amp/sq in.)^2

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. PDF 31 (printed p. 21), Table 1.1 'Magnet Design Data', TID-5215 Vol. 1

Editorial note, tabletop extrapolation: The 1.735 pole-force constant is the imperial twin of B^2/2mu0 and matches it to 1%; the hot-spot width formula is a one-line check before winding wide flat strip on a driver-amplifier-fed coil.

It was found that when the number of turns on the end coils was 50 per cent of a full coil, the field in tanks adjacent to the yokes was 4.0 per cent low.

Wakerling & Guthrie (eds.), Magnets and Magnetic Measuring Techniques — TID-5215, Radiation Laboratory, University of California (1949) — p. 139

Editorial note, tabletop extrapolation: The pattern transfers to any edge-compensation knob - outer-radius shim thickness, trim turns near a yoke window, correction-coil ampere-turns: measure the deficit at two settings, extrapolate linearly to zero as the FIRST estimate, then confirm with a third measurement - saturation and coupling bend the response, so one iteration is the hope, not the promise.

the supporting structure for the coils failed, presumably under the magnetic forces. The coils became distorted and short circuits developed.

The University of Washington 60-Inch Cyclotron: Progress and Status Report of Design and Construction — AECU-1951, University of Washington (1951) — p. 19

Editorial note, tabletop extrapolation: DIRECT at any scale: coil-on-coil and coil-on-iron forces scale with NI and B and have crushed amateur windings - brace windings as if they will be pushed, not just held up. (The outer return-path steel in UW's recovery is that machine's expedient; whether added steel raises gap field depends on where the circuit's reluctance actually sits - FEMM answers it.)

Um den Magneten nicht zu überlasten, sollte er im Dauerbetrieb höchstens mit der Hälfte des maximalen Spulenstroms betrieben werden [tr.: run at no more than half the maximum coil current in continuous duty]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 37

Editorial note, tabletop extrapolation: For any other borrowed or surplus magnet, use its actual continuous-duty specification (maximum and continuous ratings differ) and verify winding temperature under your duty cycle - half-of-maximum is this book's conservative default when no continuous rating is known. The choose-field-by-homogeneity move transfers as stated; record the chosen point as a thermal/homogeneity compromise, not a hard limit.

Im Betrieb müssen die Spulen des Magneten mit Wasser gekühlt werden. Dies geschieht durch ein (von Schülern selbst entwickeltes) Kühlsystem, das mit Hilfe einer Heizungspumpe für den notwendigen Durchfluss von ca. 10 l/min sorgt. Ein Druckausgleichsgefäß stellt den notwendigen Betriebsdruck von ca. 1 bar während des Betriebs her. Sollte das Kühlsystem einmal ausfallen, so wird der Magnet über einen Notschalter abgeschaltet. [tr.: in operation the magnet coils must be water-cooled, by a student-built cooling system whose central-heating circulator provides the necessary ~10 l/min flow; an expansion vessel maintains the ~1 bar operating pressure; should the cooling fail, the magnet is switched off by an emergency switch]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 36

Editorial note, tabletop extrapolation: Size cooling from the measured coil loss, allowable winding temperature and coolant temperature rise - the 10 l/min is this magnet's number. A fail-safe interlock (flow AND winding temperature, arranged so failure trips rather than merely alarms) is cheap against a coil rewind; whether an air-cooled coil set needs duty cycling depends on its thermal design, not its power class.

Aus dem Diagramm 5.1 liest man für diesen Strom einen Wert zwischen 300–400 mT für die Flussdichte ab [tr.: for this current one reads 300-400 mT off Chart 5.1]

Prechtl & Wolf, Das Lehr-Zyklotron COLUMBUS — Mit einem Teilchenbeschleuniger Physik und Technik erleben, Springer (2020) — p. 35-37

Editorial note, tabletop extrapolation: A home H-frame with 20 cm poles and a 3 cm gap reaches ~0.6 T with 15-20 kAT, so this surplus-magnet class is a legitimate alternative to winding your own - check the actual coil topology (series vs parallel feeds change the current arithmetic) and take B from a measurement or the manufacturer's chart at YOUR gap.

Approximately 8 kilometers of 13 gauge copper wire were wound around the six inch pole pieces for the electromagnet.

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 15

Editorial note, tabletop extrapolation: A concrete scale anchor - kilometre-class wire on a hand-wound magnet is real, with the resistance and cooling that implies - but budget a NEW magnet from its own ampere-turn requirement, winding window, current density and duty cycle; pole diameter alone doesn't set wire length.

an interlock which shuts down the magnetic if less than 2.5 liters per minute of chilled water are supplied

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 36

Editorial note, tabletop extrapolation: The transferable pattern is the method, not the numbers: independent low-flow and over-temperature interlocks wired to POWER DOWN the load, with trip points derived from the coil's insulation limits or measured thermal performance (including sensor lag) - Houghton's 2.5 L/min floor and their coil ceiling are that machine's settings, not defaults.

The magnet yoke was soft iron scrap, and the pole pieces were 11.4 cm steel round stock which were then wound with 13.5 gauge wire.

Cressman, The Design and Construction of a Small Cyclotron — Houghton College thesis (2006) — p. 16

Editorial note, tabletop extrapolation: A documented precedent that scrap return-path iron plus machined round-stock poles can serve a small machine - the machine as a whole made beam, though the survey doesn't isolate the magnet's contribution. For a new build, characterize candidate scrap (saturation, consistency, joints) and remember the return path needs cross-section, not pedigree.

A typical hybrid dipole magnet (Fig. 1) consists of DT4E poles, yokes, Sm₂Co₁₇ permanent magnet blocks, a copper trim coil, outer tuning plates, NiFe alloy plates, and aluminum structural parts. In this configuration, the PM blocks provide the main magnetic field, while the trim coil allows for fine adjustment of the field strength within a limited range. This design significantly reduces power consumption compared to traditional electromagnets, while still preserving operational flexibility. To improve adaptability, an outer iron plate mechanism is incorporated for coarse field tuning ... to address the negative temperature coefficient of permanent magnets, NiFe alloy plates are placed near the magnet poles. These act as passive compensators to stabilize the magnetic field against temperature variations

Hsu, Jan, Chu & Lin, Integrating Permanent Magnets and Electromagnets — A Hybrid Dipole Magnet Design — WEBD3, Proceedings of IPAC2025 (2025) — p. 1

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: a small PM-based magnet need not be untunable — layering a modest trim coil and a movable iron shunt onto a PM circuit restores fine and coarse adjustment within a limited range (±1.25% fine on this prototype) at a small fraction of an electromagnet's power. Enough for drift, matching and calibration; not the wide excitation range of a full coil.

The trim coil is made of 2 × 3 mm2 copper wire and contains 42 turns ... The integrated magnetic field increases by approximately 0.086% for every 1 A of coil current (Fig. 4). With a coil current range of ±15 A, the magnetic field can be adjusted by approximately ±1.25%

Hsu, Jan, Chu & Lin, Integrating Permanent Magnets and Electromagnets — A Hybrid Dipole Magnet Design — WEBD3, Proceedings of IPAC2025 (2025) — p. 2

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: a prototype calibration datum, not a scaling law — coil authority depends on gap reluctance, yoke geometry, saturation and coil placement, so compute or measure d(BL)/dI for the actual circuit. Percent-level trim on a PM-driven iron circuit is the right order for covering temperature drift; whether it also covers assembly tolerance needs a tolerance budget, not an assumption.

[Coil Data table:] Total Magnetizing force (for two coils) — 64800 Ampere-Turns; No. of coils — 02 (Top and bottom); No of turns per coil — 162; Conductor size — 10 mm x 10mm x 6 mm diameter bore (OF-OK oxygen free copper grade ASTM C10200); Operating Current — 200 A; Approximate total length of one coil — 214.5 m; Approximate weight of one coil — 135 Kg; Approximate resistance per coil — 0.05 Ohm; Approximate operating voltage (for two coils) — 20 V

IUAC, e-Tender 09/GOR/2024–25 — H-Dipole Water-Cooled DC Electromagnet for the Table-Top Cyclotron: Engineering Specification and Acceptance Tests (2024) — p. 18, 19

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: a complete, self-consistent coil design point (ampere-turns, turns, current, conductor, resistance, voltage, mass) published with enough detail to scale from — sitting just above the 0.6-1 T fields most amateur machines run. The low-voltage high-current choice (about 20 V at 200 A for ~4 kW total) shows a water-cooled hollow-conductor solution where amateur designs often accept hotter air-cooled solid-wire coils; scaling it needs the magnetic-circuit, thermal, ampacity and hydraulic calculations redone for the new geometry.

[Coil Data table:] Cooling type — Low conductivity Water cooled; Inlet cooling water pressure — 6 bar; Max Pressure drop per double pancake — 4; Water inlet temperature — 20°C (Nominal) ... Design parameters for cooling of magnet coils: Limiting value of temperature rise (deg T) of magnet coils < 40 oC; Velocity of flow in magnet coils < 3 m/sec; Pressure-drop (delta P) in magnet coils < 4 bar ... All pancake terminal water connections shall be connected with respective manifolds via proper non-conducting tube with proper pressure and temperature rating. The connectors and tubes shall have a working pressure rating at least 12 bar @ 100 oC

IUAC, e-Tender 09/GOR/2024–25 — H-Dipole Water-Cooled DC Electromagnet for the Table-Top Cyclotron: Engineering Specification and Acceptance Tests (2024) — p. 19, 23, 25

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: the working hydraulic design values for hollow-conductor magnet coils at the few-kW scale — one professional data point, not universal limits. The transferable method: parallel the water at the pancake level while the electrical circuit stays in series, and compute flow, pressure drop, temperature rise and water chemistry for the actual bore and length; every wetted component carries a pressure/temperature rating with margin (12 bar at 100 C here).

No joint in the conductor is allowed inside a pancake ... The conductor shall be wrapped with glass tape with 50% overlap to produce approximate insulation thickness of 0.5 mm turn to turn ... Electrical connections between pancakes shall be made by brazing of proper copper connectors that can carry at least 150 % of maximum current without significant heating ... The electrical connectors and bus bar (or flexible cable) that will be used for connecting two coils shall be designed and made to conduct at least 200 % of maximum current without significant heating ... brazed using silver brazing filler (at least 40% silver) ... All the water-cooled coils of magnets will be inter-turn insulated with glass tape followed by epoxy-resin impregnation & encapsulation under vacuum. The thermal class of insulation is F Class (155 oC).

IUAC, e-Tender 09/GOR/2024–25 — H-Dipole Water-Cooled DC Electromagnet for the Table-Top Cyclotron: Engineering Specification and Acceptance Tests (2024) — p. 22-24

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: a compact recipe for building reliable water-cooled magnet coils — joint placement, tape overlap, brazing alloy, connector qualification and vacuum potting — from a lab that must warranty the result. The 150/200-percent connector requirements are current-carrying thermal criteria (carry the current without significant heating), not dimensional oversizing; the no-joints-inside-a-pancake rule and those qualification margins are cheap insurance for any coil builder.

Before epoxy cast/after brazing water connectors with the pancake terminals, cooling passage of each pancake shall be tested passing with at least 5 mm diameter steel ball and documented ... [vendor compliance sheet:] Whether Bidder have Inhouse — 1. Hydrostatic Test @30 [bar] ... 2. Hydrodynamic Test @8 [bar]

IUAC, e-Tender 09/GOR/2024–25 — H-Dipole Water-Cooled DC Electromagnet for the Table-Top Cyclotron: Engineering Specification and Acceptance Tests (2024) — p. 24, 37

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: the steel-ball pass test is a zero-instrumentation way to prove a hollow-conductor bore was not crushed or blocked during winding — exactly the failure an amateur winding fixture is most likely to cause — and the source runs it before potting because epoxy makes any blockage permanent. A ball pass shows minimum clearance only; pair it with a measured flow/pressure-drop check, and derive any pressure test from the ratings of the actual fittings rather than copying the vendor-sheet values.

Insulation resistance testing: The insulation resistance between the coil terminals and mandrel using minimum voltage of 1kV DC shall be measured and noted. Insulation leakage current testing (HiPot Testing): DC voltage of 1 kV shall be applied between coil terminals and mandrel for one minute and the leakage current shall be recorded. The main coils shall be hi-pot tested at 1 kV DC for 1 minute, and it should have less than 1µA leakage to the yoke ... Coil resistance and inductance measurements shall be made with a micro-ohmmeter resistance bridge at room temperature, with the coil temperature uniform throughout and steady state conditions prevailing.

IUAC, e-Tender 09/GOR/2024–25 — H-Dipole Water-Cooled DC Electromagnet for the Table-Top Cyclotron: Engineering Specification and Acceptance Tests (2024) — p. 27

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: concrete pass/fail numbers for magnet-coil insulation testing — 1 kV, one minute, under 1 microampere — as one lab's acceptance criteria. The method transfers; the voltage does not automatically: select proof voltage from the coil's working voltage, insulation system and an applicable standard, and treat any hipot test as hazardous work — current-limited rated equipment, guarded connections, controlled ramp and dwell, and discharge before touching. Run it before the coil is bolted into an expensive yoke.

The coils will work in high ionization radiation area. Total absorbed dose in coil shall be approximately 2 MGy in its lifetime of 10 years of operation. Epoxy resin should be able to sustain the above mentioned radiation dose. Technical data sheet of radiation dose rate for the offered epoxy should be provided to IUAC.

IUAC, e-Tender 09/GOR/2024–25 — H-Dipole Water-Cooled DC Electromagnet for the Table-Top Cyclotron: Engineering Specification and Acceptance Tests (2024) — p. 23

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: a rare explicit statement of the radiation dose a design team budgets for organic insulation next to an MeV-class cyclotron gap over a decade of teaching use. Long-lived small machines should treat coil insulation as a radiation-exposed component, not just a thermal one — and note a manufacturer dose-rate data sheet alone is thin qualification: survival depends on total dose, species, dose rate, atmosphere and the property retained, so prefer total-ionizing-dose test data for the actual resin.

Thermal cut-off switches (fully insulated in a screw on housing type), set to open an electrical circuit at 40°±5°C shall be fitted on the external lead (return lead of water circuit) of each pancake ... Suitable thermal switches will be placed on outer terminals of the coils to prevent over-heating of the coils (cut-off value: > 40 oC) by shutting off the power supply ... [spec table:] Thermal sensors (cut-off value) — > 400 C (8 nos. of sensors to be mounted on each coil); Interlocks — overload, high temperature cut-off

IUAC, e-Tender 09/GOR/2024–25 — H-Dipole Water-Cooled DC Electromagnet for the Table-Top Cyclotron: Engineering Specification and Acceptance Tests (2024) — p. 19, 24, 25

Editorial note, tabletop extrapolation: Editorial note, tabletop extrapolation: hardware thermal switches on every pancake's return water lead, dropping the supply through an interlock, is a simple, software-free protection pattern for a water-cooled coil stack — with two cautions. An outlet-mounted switch lags stagnant-water and winding hot spots when flow is lost, so pair it with flow or pressure detection; and the interlock must command the supply's controlled shutdown or energy-dump path, never break magnet current mechanically — an inductive circuit interrupted dry arcs.

The Mammoflex cable is rated for 60 kV and had a capacitance of 56 pF per foot. After installation of the new supply and cable, mysterious behavior was noticed and is still not fully explained. At sufficiently high voltages (~ 30kV) arcing inside the chamber occurred – both light and audible snapping were observed. Coincident with the internal arcing, external arcing was observed between the shield of the Mammoflex cable (of the 6 foot segment between the resistor and chamber) and chassis ground, such as the magnet frame. One such arc terminated on the upper magnet coil, causing the magnet power permanent damage, requiring costly repair. The stored energy in the 6 foot cable at 30 kV is about 0.2 Joules, not much lower than the rule-of-thumb damage threshold of 1 Joule. It is also known that the focusing influence of the magnetic field can enhance the damage of an electrical discharge.

Koeth, Ponter, Hoffman, Schneider & Krutzler, Rutgers 12-Inch Cyclotron Electrostatic Deflector (2010, rev. 2011) — p. 5

Editorial note, tabletop extrapolation: The most expensive lesson in the document, and it scales down unchanged: HV cable capacitance is a stored-energy reservoir whose shield is not automatically at ground everywhere. Computing from the paper's own numbers, 56 pF/ft × 6 ft = 336 pF, and ½CV² at 30 kV is 0.15 J — the source's "about 0.2 J" at the same order (computed here). Neither 0.2 J nor the 1 J rule of thumb is a safety boundary; cable length is the variable a builder controls directly.

Linear Fit to Tapered Pole Tips' B-field at 3 Coil Currents ... y = -0.0039x + 1.1624 R² = 0.9846 ... y = -0.0033x + 1.029 R² = 0.9846 ... y = -0.0025x + 0.7587 R² = 0.9862 ... Fig.1 Radial measurements at three different magnet currents: 20, 30, & 40A

Koeth, Report on the 12-Inch Cyclotron Magnet Study: Measurements, Modeling, and Future Plans (c. 2005) — p. 3

Editorial note, tabletop extrapolation: Hard numbers for a real 12-inch H-frame's excitation curve: about 0.76 T at 20 A, 1.03 T at 30 A, 1.16 T at 40 A — the tesla-per-amp halving between steps (0.0271 vs 0.0133 T/A) is THIS iron's saturation announcing itself. Computed honestly with P = I²R at fixed resistance: the 30→40 A step buys its 0.133 T at about 2.85× the incremental copper power per tesla of the 20→30 A step (700R/0.133 versus 500R/0.271). The fit slope is the normalized radial FIELD gradient, about −0.34% of central field per inch at 40 A — not the physical pole-taper angle. Where another magnet's payback ends is its own B(i) curve's business. (Fit values and R² read from the rendered Fig. 1; the 20/30/40 A assignment follows the curve intercepts, since the printed legend order is 30, 20, 40.)

The coil current density was empirically set. The construction of the actual 12-inch cyclotron coils is unknown, as the coils came from a surplus source. The current density was varied in PSF through several points, until the peak 1.22 Tesla was achieved in the center of the gap. This corresponded to a PSF setting of 30,000 Ampere-turns. ... A comparison of PSF’s output with the linear portion of the actual measured B(i) curve can yield insight into the construction of the coils, which was determined to be about 850 windings per coil.

Koeth, Report on the 12-Inch Cyclotron Magnet Study: Measurements, Modeling, and Future Plans (c. 2005) — p. 5

Editorial note, tabletop extrapolation: A recoverable-datasheet method for surplus coils: fit a magnetostatics model's excitation until it reproduces the measured field, then read effective turns from matched ampere-turns over the linear region — N = (fitted A-turns)/I, with the per-coil-versus-total convention stated explicitly, which this memo leaves ambiguous: 30,000 A-turns over 850 turns implies ~35 A on a per-coil reading, while the document's stated ~32 A nominal (dg-1687) with 850 turns gives 27,200 — a bookkeeping tension to resolve on your own magnet, not an error to copy. The 850 turns is the inferred construction of THESE coils, not sizing guidance.

Fig.6 PSF B(i) curve, note lack of saturation ... Fig.7 Actual measured B(i) curve

Koeth, Report on the 12-Inch Cyclotron Magnet Study: Measurements, Modeling, and Future Plans (c. 2005) — p. 5

Editorial note, tabletop extrapolation: A cautionary pair at the target scale: the same 2-D model that matched the measured radial field SHAPE missed the excitation curve's saturation knee entirely — as run, evidently without material nonlinearity doing its job. The correct lesson is narrower than 'knees cannot be modeled': a nonlinear 2-D solve with a real B-H curve can capture saturation (3-D leakage it cannot), so give the code proper steel data, then validate BOTH B(i) and the field shape against measurement through the knee. (Measured curve endpoints — roll-over above ~0.03 kA, ~1.17 T at 0.05 kA — read from the rendered Fig. 7, whose x-axis is printed in kA.)

The cyclotron facility has already secured an H-frame 19-inch magnet, a special General Electric magnet delivered to Rutgers in 1947 … and operated for 35 years for NMR research before retirement to storage.[13] Upon acquisition, the venerable magnet coils were in need of refurbishing and are currently awaiting new copper windings. … Future plans include the assembly of a second generation 19-inch educational cyclotron.

Ruisard, Hine, Koeth & Rosenberg, The Rutgers Cyclotron: Placing Student's Careers on Target — WE1PB02, Proceedings of Cyclotrons2013 (2013) — p. 5

Editorial note, tabletop extrapolation: PDF p.5 = printed p.295. One documented acquisition route: a decommissioned 1947 GE NMR electromagnet, secured for a planned second-generation educational machine — with the coils needing refurbishment as part of the price. It also records the scale step this program judged worth taking from a proven 12-inch: 19 inches, not 30. Before buying any surplus magnet of that vintage, inspect winding insulation, cooling passages, resistance and field quality; rewinding is a real possibility, not a certainty. This was a plan in 2013; the paper reports no beam from the 19-inch machine.

One such arc terminated on the upper magnet coil, causing costly damage to the magnet power supply.

Koeth, Rosenberg, Krutzler, Ponter, Schneider & Hoffman, Rutgers 12-Inch Cyclotron: Dedicated to Training Through Research and Development — WEPPT024, Proceedings of Cyclotrons2013 (2013) — p. 3

Editorial note, tabletop extrapolation: PDF p.3 = printed p.368. A concrete, expensive failure chain for anyone adding HV to an existing machine — and it is two-stage: the internal deflector discharge excited the charged cable (the Blumlein mechanism, dg-1826), and the resulting EXTERNAL arc terminated on the magnet coil and took out the magnet supply. The warning that transfers: HV transients couple into unrelated subsystems through cabling, grounds and stray capacitance, so an HV fault must be analyzed as a whole-machine event, not a deflector event.

The magnet’s upper and lower coils are independently energized for intentional field imbalance so as to shift the median plane. … Figure 6 shows three standard radial-draw beam images: the left frame top/bottom coil at 17/12 amps, the middle frame at 14.5/14.5 amps, and the right frame at 12/17 amps.

Koeth, Beam Physics Demonstrations with the Rutgers 12-Inch Cyclotron — WEPPT025, Proceedings of Cyclotrons2013 (2013) — p. 3

Editorial note, tabletop extrapolation: PDF p.3 = printed p.371 (design intent on PDF p.1 / printed p.369). A genuinely cheap axial-steering mechanism for a small machine: energize the two coils independently and trim the median plane. On this machine a 5 A top-to-bottom imbalance about the 14.5/14.5 A balance point still brought beam to the periphery — a demonstration that the knob has useful range, with transmission, centering and beam quality at each setting still to be measured on any machine that copies it.

The magnet weighs 1780 pounds, it requires 40 volts at 168 amps, 7Kilowatts, to produce the maximum field of 1.2 Tesla. Only 28 volts at 114 amps, 3.2 kW, is required at the operating value of 0.889 Tesla. Water cooling is used to remove the heat generated by the coils, the inlet pressure is approximately 38 PSI and flow rate is no less than 4 GPM. The pressure is controlled with an inline pressure regulator and the flow rate is monitored with an impeller driven magnetic pick-up digital flow meter.

Koeth, The Construction and Operation of a Nine Inch Cyclotron (undated scan; the machine ran 1995–1999) — p. 1

Editorial note, tabletop extrapolation: The most useful sizing datum in the document: backing off from 1.2 T to the 0.889 T operating point cut coil dissipation from 6.7 kW (40 V × 168 A; the author's "7Kilowatts" is rounding) to 3.19 kW — a factor of about 2.1 — while still requiring monitored water cooling (38 PSI, ≥4 GPM, flow meter). The shape of the lesson transfers (field costs quadratic-ish power near saturation; margin is cheap to buy by backing off), the numbers belong to this 1780-pound magnet.